Learn How To Rotate An Object 90 Degrees Counterclockwise: Step-By-Step Guide With Rotation Matrix

Rotation 90 degrees counterclockwise

This is an example of this rigid motion transformation.

To rotate an object 90 degrees counterclockwise, follow these steps:

1. Draw a coordinate system around the object: Draw a set of lines that intersect at the center of the object to create a coordinate system.

2. Choose the axis of rotation: The axis of rotation is the line around which the object will rotate. In this case, the axis of rotation will be the line that intersects at the top left and bottom right corners of the object.

3. Rotate the object: To rotate the object, you need to move each point of the object to its new position. Start with the point at the top left corner of the object.

a. Apply a rotation matrix: Use a 2×2 matrix to transform the point. The matrix for 90-degree counterclockwise rotation is:

[ cos(θ) sin(θ) ]

[-sin(θ) cos(θ) ]

where θ = -90°.

b. Apply the matrix to each point: Multiply the matrix with each point of the object to get its new position in the coordinate system.

4. Verify the new position: Check the position of each point in the new coordinate system. The object should be rotated 90 degrees counterclockwise around the chosen axis of rotation.

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